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Taya2010 [7]
3 years ago
13

Determine the angle between the lines y=4x+2 and y=-x+3.

Mathematics
1 answer:
kotykmax [81]3 years ago
4 0
The vector v_1=(4,1) is parallel to the line  y=4x+2
and the vector  v_2(-1,1)  is parallel to the line  y=-x+3.
On one hand  v_1v_2=(-1)4+1^2=-3.
On the other hand  
v_1v_2=\vert v_1\vert\vert v_2\vert cos\theta\\=\sqrt{17}\sqrt{2}\cos\theta

Equating we get  \sqrt{34}\cos\theta=-3.
so  \theta=\cos^{-1}\dfrac{-3}{\sqrt{34}}=120\text{ degrees}
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